Murray, who is currently Asda owner Walmart’s senior vice-president of creative and customer experience, will join Asda’s board on 15 February.
Murray’s arrival at Asda coincides with the supermarket’s Project Renewal, which it describes as a "blueprint for the future of the business designed to consolidate its position as the UK’s lowest price full range supermarket".
He joins the supermarket’s executive board, which has been created by Asda chief executive Andy Clarke.
While at Walmart, Murray worked on an array of marketing and customer-facing innovations. Before that he held marketing and technology posts at companies including Hallmark and P&G.
He has worked agency-side too, and was the founder of shopping marketing agency Saatchi & Saatchi X.
Clarke said: "Keeping ahead of what our customers want by recognising when their needs change and adapting how we do things is the cornerstone of Project Renewal.
"It will mean that we can deliver low prices with great quality without compromising the financial stability of our business."
He added: "[Murray's] deep understanding of global retail trends, creative marketing and customers’ shopping habits will bring a new dimension to our strategy to overhaul our offer, merchandising and value proposition and transform of our stores, starting with the largest 95 stores."